My Stanford Encyclopedia entry on the Church-Fitch paradox of knowability (coauthored with Berit) was recently updated and is now online.
September 22, 2008
September 08, 2008
Vincent Hendricks and Duncan Pritchard just published a really fun book of interviews with leading epistemologists. It's called Epistemology: 5 Questions. Here are the 5 questions:
- Why were you initially drawn to epistemology (and what keeps you interested)?
- What do you see as being your main contributions to epistemology?
- What do you think is the proper role of epistemology in relation to other areas of philosophy and other academic disciplines?
- What do you consider to be the most neglected topics and/or contributions in contemporary epistemology?
- What do you think the future of epistemology will (or should) hold?
Posted by Joe Salerno at 1:37 PM
August 18, 2008
June 20, 2008
Yesterday Trenton Merricks gave a great talk on Truth and Freedom. He argued that a class of fatalist arguments of the form below are question begging and that their first premise is false.
1. It was true a thousand years ago that Jones sits at time t (where t is a few moments from now), and Jones has no choice about that fact.
2. Necessarily, if it was true a thousand years ago that Jones sits at t, then Jones sits at t.
3. Jones has no choice about his sitting at t.
He demonstrated his point by replacing all occurrences of 'was true a thousand years ago' with 'will be true a thousand years from now'.
My own reaction is that both arguments are invalid. They fallaciously rest on the principle that failing to have a choice (regarding the truth of a proposition) is closed under necessary implication. Let NC be the factive operator 'has no choice that', so that 'sNC(p)' says 'it is true that p, but person s has no choice about it'. Then the above argument has the following form:
2*. Necessarily, p implies q.
We see that this is an instance of the closure principle. But counterexamples to the principle are not hard to find. Let p be the true proposition that person A at time t has tortured some detainees at Gitmo. B clearly has no choice about p (because B doesn't know about A's activities). But our proposition (that p) necessarily implies that somebody at some time tortured some detainees at Gitmo. It would follow by the above argument that B had no choice about whether somebody at some time was tortured at Gitmo. However, B himself tortured some detainees there, and so did in fact have a choice about whether some detainees were tortured.
A defense of the Merricks analysis over the one favored here might include the following objection. Even though B had a choice about torturing detainees he did in fact torture, he didn't have a choice about whether some detainees were tortured. After all, he had no choice about what others would do without his knowledge, and those others happened to torture some people. The problem with this objection is that it entails that neither A nor B had a choice about whether some detainees were tortured (even though, we may suppose, A and B were the only ones willfully torturing). More generally, nobody ever has a choice about any existential proposition that more than one person makes true! In sum, if we supposed NO-Choice is closed under necessary implication, we've already conceded too much to the fatalist.
Posted by Joe Salerno at 2:04 PM
May 07, 2008
April 11, 2008
Couple great epistemology conferences approaching in Madison:
Wisconsin Epistemology Workshop is taking place on the UW-Madison campus May 3-4, featuring Earl Conee, Richard Feldman, Ernie Sosa, Alvin Goldman, Timothy Williamson, and (as commentator) Jim Pryor. This conference is organized by Juan Comesana, and is sponsored by The Anonymous Fund and the Berent Enc fund of the UW-Madison Philosophy Department.
The Fifth Annual Formal Epistemology Workshop takes place on the UW-Madison campus May 15-18. The workshop is sponsored by the Philosophy Departments at UW-Madison, Berkeley, UT-Austin, and Carnegie Mellon.
[HT: Sandy Goldberg]
Posted by Joe Salerno at 3:06 PM
April 07, 2008
My issue of Synthese is now finalized. I've included below the contents and a link to my introduction. I expect it to go into production in the near future.
SYNTHESE: Knowability and Beyond
- Editor's Introduction
- "Williamson's Woes" Neil Tennant (OSU)
- "Antirealism and Universal Knowability" Michael Hand (Texas A&M)
- "Possible Knowledge of Unknown Truth" Dorothy Edgington (Oxford)
- "Knowability and the Capacity to Know" Michael Fara (Princeton)
- "Fitch's Paradox and Ceteris Paribus Modalities" Carlo Proietti (Paris) and Gabriel Sandu (Paris)
- "The Incarnation and the Knowability Paradox" Jonathan Kvanvig (Baylor)
- "Necessary Limits to Knowledge: Unknowable Truths" Richard Routley Sylvan (ANU) [REPRINT]
Posted by Joe Salerno at 8:08 PM
February 20, 2008
In “Modals and Conditionals Again” Angelica Kratzer treats natural language ‘must’ as the expression of a two-place relation between a premise set and a proposition. The trick is getting the relation straight. Consider the following 'must' claims:
Deontic: “One must not microwave kittens!”
Doxastic: “In light of what Jack mistakenly believes, Jill must be in love with him.
Epistemic: “Oh…, the gun must have been loaded.”
Dispositional: “If you must smoke, then please use an ashtray (and not my rhododendra)”
Bouletic: “You must wear that fabulous dress”
For Kratzer the two-place relation is 'must in view of', giving
Deontic: “In view of our duties, one must not incinerate kittens”
Doxastic: In view of what Jack mistakenly believes, Jill must be in love with him.
Epistemic: “In view of what we now know, the gun must have been loaded.”
Dispositional: “If, in view of what you are disposed to do, you must smoke, then use an ashtray”
Bouletic: “In view of what my preferences state, you must wear that fab dress”
The natural way to read these claims is as follows:
p follows from A.
And the corresponding dual operator 'can' is read:
p is compatible with A.
Two well-known problems emerge for this sort of semantics. First it forces a vacuous reading of 'must' claims that relate a proposition to an inconsistent premise set. And second, it gives rise to all sorts of unwelcome modal collapses, and relatedly, forces a vacuous reading of 'must' claims that relate non-contingent propositions to premise sets. In my talk at Kioloa, I criticized a proposal by Kratzer for dealing with the first problem. I then argued that the two problems are related and sketched a unified solution.
Kratzer's proposal tells us that ‘musts’ and ‘cans’ follow from the appropriate consistent subsets of the given premise set. More specifically, let A be an inconsistent premise set of, say, legal judgments.
each set in X has a superset in X from which p follows.
The problem with inconsistent premise sets, of course, is that they entail everything. However, it is false that each set in X has a superset in X from which an arbitrary proposition follows. So, unlike the natural proposal with which we began, Kratzer's proposal doesn't predict the absurd claim that, in view of the law, we must commit murder.
However, the restriction not only blocks the application of 'must' to arbitrary propositions, but it blocks the application of 'must' to any contradicted premise. So claims like the following are predicted to be false:
"In view of what Graham believes, the Liar sentence must be true"Moreover, Kratzer's proposal always blocks the application of 'must' to premises responsible for the inconsistency and it sometimes blocks the application of 'must' to important consequences that (at least partially) depend on at least one of the contradicted premises.
"In view of what Graham believes, the Liar sentence must not be true".
Here's an example of the latter type of case. White House chief of staff “Scooter” Libby was convicted of obstruction of justice and making false claims to federal investigators during the CIA leak investigation. Bush commuted his prison sentence from 33 months to 0 on the grounds that any term of imprisonment for such nonviolent first offenses by experienced government service employees is too harsh. This contradicts US federal sentencing guidelines and practice, which prescribe hard time for such offenders. In view of federal sentencing guidelines, what now must be prescribed for the sentencing of a like criminal c for like crimes? It would be irresponsible to let Bush’s incompetence and nepotism overly influence the federal justice system. Hence, in view of federal sentencing guidelines, c must do hard time.
But Kratzer’s view doesn’t predict this. For it depends on at least one contradicted legal judgment---viz., criminals of this sort are to do hard time. And when that is the case, it will be false that, for each consistent subset of the sentencing guidelines, there will be a superset among them from which it follows that c is to do hard time.
A second problem with the Kratzer proposal is that it says nothing about what to do when the proposition p fails to be a contingent matter. When p is necessarily true, then it follows from every set. Therefore, in every context, p must be the case. For instance, the view predicts that, in view of what Michael (the intuitionist) believes, excluded middle is correct. But Michael the intuitionist denies the unrestricted truth of excluded middle. To pick another example of this kind, we want to say that Obama might actually win in November. But suppose in fact Hillary wins. Then in view of what we know it must be that Hillary actually wins. That's because 'Hillary actually wins' is necessarily true (if true). So, in view of what we know, it must be that actually Hillary will win. But then, by the duality of the operators, it is false that in view of what we know Obama might actually win.
The problem of inconsistent premise sets and the problem of collapsed modals are at root the same problem. In each case we assume that the deontic/doxastic/epistemic/legal/bouletic "possibilities" are a subset of the logical possibilities. And that is not how it should be. After all, in view of what we know, it may be that Goldbach’s conjecture is false. Ex hypothesi, it’s true. And, for all we knew before the telescope, Hesperus might not have been Phosphorus. And, for all we know right now, Obama might actually be the next US president. Ex hypothesi, Clinton wins.
The view I proposed in Kioloa was this:
all the relevantly similar (possible or impossible) A-worlds are p-worlds.
'In view of A, it can be that p' is true
some relevantly similar (possible or impossible)
A-worlds are p-worlds.
I treat 'musts' as counterfactuals because the corresponding strict conditional, which would quantify over all possible and impossible worlds, would be too strong and rarely (if ever) come out true. The corresponding 'can' claims would be too weak and would usually (if not always) come out true. The important insight is that, with the introduction of impossible worlds, we drop the assumption that the relevant accessibility relation is a subset of S4/S5 accessibility. In so doing, we block the familiar modal collapses and the special problems of inconsistent premise sets, and we get that much closer to the correct understanding of 'must and 'can'.
Posted by Joe Salerno at 8:52 PM
February 19, 2008
Patrick Greenough argued that Stanley's certainty account of assertion doesn't work. Among the counterexamples were warranted assertions of future contingents, for which the relevant brand of certainty is virtually impossible to achieve.
I responded to some of Angelica Kratzer's recent work on 'must' and 'can'. Kratzer thinks about 'must' claims as 'must in view of claims'. (Will post on some of this soon.) The view I defended was this: 'In view of premise set A, it must be that p' is true iff 'p' is true at all the relevantly similar (possible or impossible) A-worlds. This gives us the right predictions for cases of inconsistent premise sets and awkward cases where p is not a contingent matter (e.g., "in view of what Dummett believes it must be that excluded middle is false").
Yuri Cath argued against the view that knowledge-how is a species of knowledge-that. The strategy was to construct cases of knowledge-how (e.g., knowledge how to juggle) for which the relevant corresponding beliefs (e.g., that w is a way to juggle) are Gettiered or corresponding justification for such beliefs is defeated.
Brent Madison discussed the question of whether causation is necessary for epistemic basing. He argued that contrary to what is presupposed in much of the literature on basing relations, Lehrer's case of the gypsy lawyer doesn't undermine the requirement.
Stephen Hetherington disagreed with the orthodox belief that all Gettier cases are cases of knowledge failure. The discussion was driven by a pretheoretic intuition about the kind of luck that generates Gettier's original cases.
Declan Smithies defended a JJ-principle---viz., one is justified in believing p only if one is justified in believing that one is justified in believing that p. He argued that it explains various Moorean paradoxes and the role of justification in critical reflection.
Dave Chalmers sought an epistemic constraint on truth that avoids the Church-Fitch paradox of knowability. Dave takes it that each basic truth is knowable by somebody. Let 'b' express the conjunction of all the basic truths. All non-basic truths are knowable in the sense that someone is in a position to know that p is materially implied by b.
Daniel Star defended his view that a fact X is a reason for an agent N to F just when X is evidence that N ought to F.
Berit discussed the knowledge argument (construed as an argument against a priori physicalism). She defended it against a number of objections, including the old fact reply and the missing concepts reply.
Wolfgang Schwartz took issue with the standard interpretation of Frank Arntzenius' example of the traveler who in fact passed the mountains on her way to Shangri-La. It is usually treated as a case where the traveler must eventually update to .5 her credence that she came by way of the mountains, lest she violate the principle of Indifference. Wo, by contrast, defended the view that she should retain the credence she had when passing the mountains (viz. 1), lest she violate Conditionalization and Reflection.
Jonathan Schaffer closed the workshop with a paper about a brand of skepticism which threatens the broadest range of knowledge. Knowledge entails basing. Hence, any knowledge (even a priori knowledge and the cogito) is threatened by the debasing demon who, at the final stage of the basing process, intervenes to make it the case that the otherwise properly based belief is based on a guess or wishful thinking. The demon covers his tracks by leaving the victim with no indication that the normal process has been tampered with.
Posted by Joe Salerno at 10:58 AM
February 15, 2008
Epistemology at the Beach is a workshop this weekend hosted by Dave Chalmers' Centre for Consciousness and Daniel Stoljar's Basic Knowledge grant and organized by Declan Smithies. The location is the ANU Coastal Campus. I'll try to blog the event.
Participants: Jonathan Schaffer, Patrick Greenough, Berit Brogaard, Joe Salerno, Brent Madison, Yuri Cath, Wolfgang Schwartz, Declan Smithies, Daniel Star, David Chalmers, Stephen Hetherington, Daniel Stoljar, Susanna Schellenberg, David Bourget, Aisling Crean, JC Bjerring, John Cusbert, Holly Lawford-Smith, Masafumi Matsumoto, Doug Edwards, Federico Luzzi, Paul Dimmock, Grant Reaber, Fiona MacPherson and Stuart X.
Patrick Greenough: Assertion, Knowledge and Certainty
Joe Salerno: Must and Can
Yuri Cath: Knowing How Without Knowing That
Brent Madison: Causation and the Epistemic Basing Relation
Stephen Hetherington: Gettiered Knowledge
Declan Smithies: Critical Reflection and Epistemic Responsibility
David Chalmers: Knowability and Scrutability
Daniel Star: Reasons: Explanations or Evidence?
Berit Brogaard: On the Knowledge Argument
Wolfgang Schwartz: I’m Certain That I Went By The Mountains
Jonathan Schaffer: The Debasing Demon
Posted by Joe Salerno at 1:56 AM
February 05, 2008
January 21, 2008
What I did in my commentary at the Eastern APA is frame a debate about Fitch's paradox, and explain the significance of Salvatore Florio and Julien Murzi’s contribution to the intuitionistic reply. Along the way I tried to improve on their main argument.
Consider the following epistemic theories of truth, which are supposed to differ
precisely on the strength of the advertised relation between truth and knowledge.
Semantic Idealism (SI): p(p Kp)
Necessarily, all truths are in fact known (by some finite being at some time).
Strict Finitism (SF): p(p FKp)
Necessarily, all truths are feasibly knowable = necessarily, all truths are are knowable by beings who have precisely the cognitive capacities that we at some time happen to have.
Moderate Anti-realism/Weak Verificationism (WVER): p(p Kp)
Necessarily, all truths are knowable by us in principle (i.e., by beings whose capacities are at best finitely better than those we happen to have).
And consider the following brand of realism, which denies all three positions.
Realism (R): p(p & ~Kp)
There may be unknowable truths---i.e., truths that couldn’t be known given any finite extension of our cognitive capacities.
The three brands of anti-realism appear to be listed in the order of their logical strength, from strongest to weakest. (SI) entails (SF) entails (WVER), and the entailments are not meant to go the other way. Indeed, (WVER) gains its plausibility to the extent that it can distance itself from awkward forms of idealism and strict finitism.
The Church-Fitch paradox is a proof that threatens to show that moderate antirealism collapses into idealism. A classical formulation of Florio and Murzi’s paradox of idealization (presented at the APA) threatens to show that (WVER) collapses into (SF). The lesson of either is that so-called "moderate anti-realism" is an inherently unstable position. In the context of that epistemic theory of truth, the apparently modest idealization is equivalent to at least one of the immodest idealizations. Simply put, a so-called moderate anti-realist can’t distinguish between actual knowledge, feasible knowability, and knowability in principle.
I put the lessons this way for simplicity of exposition, although stating them as I
have presupposes excluded middle. The Florio-Murzi proof aims to draw related lessons without excluded middle, and thereby aims to show that an independent commitment to intuitionistic logic can't rescue the moderate anti-realist from the grips of Fitch-like paradoxes.
The key concept in the Florio-Murzi discussion is the concept of an ideal agent. They define it as any finite agent whose epistemic capacities are better than our own. Their proof requires that it be a priori that there are no ideal agents. Since humans may be cosmic hicks, as it were, F and M must not mean "human capacities" by "our capacities". After all, it is an a posteriori matter whether there are beings in the universe with epistemic capacities better than those of humans. So I take it that by 'ideal agent' they mean any finite agent whose capacities are better than any actual finite agent. This provides the desired strength to the first premise of the Florio-Murzi proof:
1. There are no ideal agents.
The second and most critical assumption in the Florio-Murzi proof is that
there is a truth q that isn’t feasibly knowable. Indeed, their assumption requires that it be necessary that anyone who knows q is an ideal agent. Call this assumption epistemic modesty. It is presumed that even the moderate intuitionistic anti-realist is epistemically modest in this sense.
2. (Epistemic Modesty) There is a feasibly unknowable truth; that is, a truth such that necessarily any being that knows it is ideal:
q(q & x(Kxq Ix))
Epistemic modesty is meant to be a more precise denial of Strict Finitism. F and M foreshadow the following kind of objection to (Epistemic Modesty). Can't we have a cognitive twin in a world with a more favorable set of epistemic resources or environment? In such a world subjects with our cognitive capacities are in a position to know q, even though we in the actual world are not. Beings internally like us, but in improved external circumstances, acquire knowledge more easily than we do. For instance, suppose that cognitive limitations prevent any actual being from determining the location of a particular distant star. Nevertheless, there will be possible worlds where our telescopes are better or the cosmic environment for whatever reason better preserves the brightness of stars over longer distances. In such worlds, beings with precisely our cognitive capacities come to know a truth that is feasibly unknowable in the actual world.
Such considerations threaten the plausibility of (Epistemic Modesty). I don’t believe that Florio and Murzi said enough in their paper to dispel the worry. But here is a quick fix. Redefine an ideal agent more generally as one who has a finitely improved epistemic state of information, where states of information include the subject’s cognitive capacities, resources and environment. And let q be a truth that can’t be known by beings in any actual epistemic state of information. Then (Epistemic Modesty) is more intuitive. When q is a truth that we're not in a position to know (owing to our cognitive, material and environmental limitations), then by definition knowing q necessitates being in a better epistemic state. That is, necessarily, if x knows q then x is an ideal agent in that she is epistemically better off---i.e., she has either increased cognitive capacities, better epistemic resources, or a more epistemically friendly environment.
With these adjustments the Florio-Murzi proof is much stronger. It has the following structure. Assumptions I through III entail a contradiction:
I. (No Ideal Agents) There are no ideal agents.
II. (Epistemic Modesty): There is a feasibly unknowable truth.
q(q & x(Kxq Ix))
III. (WVER): All truths are knowable in principle.
An illuminating version of the proof goes like this:
|0||0. p(p Kp)|| [WVER]|
|1||1. ~xIx|| [No Ideal Agents]|
|2||2. q|| [A for CP]|
|3||3. x(Kxq Ix)|| [A for Reductio]|
|3||4. x(Kxq Ix)|| [from 3]|
|3||5. Kaq Ia|| [from 4]|
|6||6. Ka(q & ~xIx)|| [A for reductio]|
|6||7. Kaq & Ka~xIx|| [6 by K-distributivity]|
|6||8. Kaq|| [from 7]|
|3,6||9. Ia|| [from 5 and 8]|
|3,6||10. xIx|| [from 9]|
|6||11. q & ~xIx|| [6 by K-factivity]|
|6||12. ~xIx|| [from 11]|
|3,6||13. Contradiction|| [from 10 and 12]|
|3||14. ~Ka(q & ~xIx)|| [6-13 by reductio]|
|3||15. ~Ka(q & ~xIx)|| [from 3, 4-14, since only necessities follow from necessities]|
|3||16. ~Ka(q & ~xIx)|| [15 by def. of ]|
|0||17. (q & ~xIx) Ka(q & ~xIx)|| [from 0]|
|0,3||18. ~(q & ~xIx)|| [from 16, 17]|
|1,2||19. q & ~xIx|| [from 1, 2]|
|0,1,2,3||20. Contradiction|| [18, 19]|
|0,1,2||21. ~x(Kxq Ix)|| [3-20 by Reductio]|
|0,1||22. q ~x(Kxq Ix)|| [2-21 by CP]|
|0,1||23. q(q ~x(Kxq Ix))|| [22 by -Intro]|
|24||24. q(q & x(Kxq Ix))|| [Epistemic Modesty]|
|0,1,24||25. Contradiction||[from 23 and 24]|
As F and M point out, the proof is intuitionistically valid. However, I don’t think it gains any ground, over and above Fitch's paradox, against the intuitionistic strategy. The intuitionist is happy to deny the epistemic modesty principle---i.e., that there are feasibly unknowable truths:
i. ~q(q & x(Kxq Ix))
After all, existence for the intuitionist is constructive existence, and we can’t construct an example of a feasibly unknowable truth.
The typical charge against this sort of maneuver is epistemic hubris. But the typical reply is for the intuitionist to regain her modesty by replacing the original modest assumption with a claim that is classically but not intuitionistically equivalent. For instance, she might deny that every truth is feasibly knowable:
ii. ~q(q x(Kxq & ~Ix))
Classically i. and ii. contradict. But not intuitionistically. There are more intuitionistic distinctions than there are classical distinctions, and the intuitionist usually takes advantage of this fact. Contrary to what I thought at the APA, the move won't work in this case, since ii contradicts line 23 of the proof. Line 23 rests only upon WVER and No Ideal Agents.
The intuitionist at this point might chose some other more complicated classically (but not intuitionistically) equivalent formula with which to express her modesty. Surely there is at least one that doesn't intuitionistically contradict line 23. The move should be followed with an explanation of why this, rather than the original formula, best expresses her epistemic modesty.
There is, however, a recommendation to preempt this intuitionistic maneuver. It is based on a suggestion raised by F and M in their paper. First and foremost, don’t assume the existence of a feasibly unknowable truth. Instead begin with a proposition that would be feasibility knowable, regardless of its truth value. For instance, let q be the sentence ”There is life on x”, where x is some planet that is epistemically inaccessible in the relevant sense. Our cognitive capacities, or overall epistemic state of information, is inadequate for the determination of whether or not q. So we should be modest about q and about ~q. The commitment is to a proposition q such that: necessarily if an agent knows q then she is ideal, and necessarily if an agent knows ~q then she is ideal.
iii. x(Kxq Ix)
iv. x(Kx~q Ix)
Notice that we don’t presuppose the constructive existence of a feasibly unknowable truth. But we still get a contradiction. Line 23, which rests just on WVER and NO IDEAL AGENTS, shows us that the assumption q together with iii jointly entail a contradiction. Hence, ~q. And by analogous reasoning ~q and iv jointly entail a contradiction.
If the intuitionist already has some other way of expressing her modesty she can give up at least one of iii and iv. She is still not committed to Strict Finitism, but she will be committed to some principle classically, but not intuitionistically, equivalent to Strict Finitism. There is logical space for her to do so. But she will have to tell some complicated story to regain an epistemically modest footing.
Contrary to what I thought at the APA, I don't believe that the Florio-Murzi paradox of idealization raises new difficulties for moderate intuitionistic anti-realism---that is, difficulties over and above those already raised by the Church-Fitch paradox. However, I think it highlights the significance of knowability paradoxes more generally. Such paradoxes show us that if we treat truth as an epistemic notion, then we blur modal epistemic distinctions that are needed to make such theories plausible.
Posted by Joe Salerno at 1:39 PM